Functional pearl: I am not a number - I am a free variable

Proceedings of the ACM SIGPLAN 2004 Haskell Workshop, Haskell'04

Volumn , Issue , 2004, Pages 1-9

  McBride, Conor ^a   McKinna, James ^b  

^a DURHAM UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

Abstract syntax; Bound variables; De Bruijn representation; Free variables; Fresh names; Haskell; Implementing Epigram; Induction principles

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER PROGRAMMING; COMPUTER PROGRAMMING LANGUAGES; DATA REDUCTION; FORMAL LOGIC; HIERARCHICAL SYSTEMS; PARAMETER ESTIMATION;

ABSTRACT SYNTAX; BOUND VARIABLES; DE BRUIJN REPRESENTATION; FREE VARIABLES; FRESH NAMES; IMPLEMENTING EPIGRAM; INDUCTION PRINCIPLES;

SYNTACTICS;

EID: 11244266030     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. T. Altenkirch and B. Reus. Monadic presentations of lambdaterms using generalized inductive types. In Computer Science Logic 1999, 1999.
2. F. Bellegarde and J. Hook. Substitution: A formal methods case study using monads and transformations. Science of Computer Programming, 1995.
3. R. Bird and R. Paterson. de Bruijn notation as a nested datatype. Journal of Functional Programming, 9(1):77-92, 1999.
4. T. Coquand. An algorithm for testing conversion in type theory. In Huet and Plotkin [11].
5. N. G. de Bruijn. Lambda Calculus notation with nameless dummies: a tool for automatic formula manipulation. Indagationes Mathematics:, 34:381-392, 1972.
6. F. de Saussure. Course in General Linguistics. Duckworth, 1983. English translation by Roy Harris.
7. P. Dybjer. Inductive Sets and Families in Martin-Löf's Type Theory. In Huet and Plotkin [11].
8. G. Gentzen. The collected papers of Gerhard Gentzen. North-Holland, 1969. Edited by Manfred Szabo.
9. G. Huet. The Constructive Engine. In R. Narasimhan, editor, A Perspective in Theoretical Computer Science. World Scientific Publishing, 1989. Commemorative Volume for Gift Siromoney.
10. G. Huet. The Zipper. Journal of Functional Programming, 7(5):549-554, 1997.
11. G. Huet and G. Plotkin, editors. Logical Frameworks. CUP, 1991.
12. T. Johnsson. Lambda Lifting: Transforming Programs to Recursive Equations. In Jouannaud [13], pages 190-203.
13. J.-P. Jouannaud, editor. Functional Programming Languages and Computer Architecture, volume 201 of LNCS. Springer-Verlag, 1985.
14. S. Kleene. Introduction to Metamathematics. van Nostrand Rheinhold, Princeton, 1952.
15. Z. Luo. Computation and Reasoning: A Type Theory for Computer Science. Oxford University Press, 1994.
16. C. McBride. Inverting inductively defined relations in LEGO. In E. Giménez and C. Paulin-Mohring, editors, Types for Proofs and Programs, '96, volume 1512 of LNCS, pages 236-253. Springer-Verlag, 1998.
17. C. McBride. Elimination with a Motive. In P. Callaghan, Z. Luo, J. McKinna, and R. Pollack, editors, Types for Proofs and Programs (Proceedings of the International Workshop, TYPES'00), volume 2277 of LNCS. Springer-Verlag, 2002.
18. C. McBride. Epigram, 2004. http://www.dur.ac.uk/CARG/epigram.
19. C. McBride and J. McKinna. The view from the left. J. of Functional Programming, 14(1), 2004.
20. J. McKinna and R. Pollack. Pure type systems formalized. In M. Bezem and J.-F. Groote, editors, Int. Conf. Typed Lambda Calculi and Applications TLCA'93, volume 664 of LNCS. Springer-Verlag, 1993.
21. J. McKinna and R. Pollack. Some lambda calculus and type theory formalized. Journal of Automated Reasoning, 23:373-409, 1999. (Special Issue on Formal Proof, editors Gail Pieper and Frank Pfenning).
22. D. Miller. Unification under a mixed prefix. Journal of Symbolic Computation, 14(4):321-358, 1992.
23. R. Pollack. Closure under alpha-conversion, In H. Barendregt and T. Nipkow, editors, Types for Proofs and Programs, LNCS 806, pages 313-332. Springer-Verlag, 1994. Selected papers from the Int. Workshop TYPES '93, Nijmegen, May 1993.
24. R. Pollack. Closure under alpha-conversion, In H. Barendregt and T. Nipkow, editors, Types for Proofs and Programs, LNCS 806, pages 313-332. Springer-Verlag, 1994. Selected papers from the Int. Workshop TYPES '93, Nijmegen, May 1993.
25. D. Prawitz. Natural Deduction - A proof theoretical study. Almquist and Wiksell, Stockholm, 1965.
26. P. Wadler. How to Replace Failure by a list of Successes. In Jouannaud [13], pages 113-128.